THE OTHER HIGGSES, AT RESONANCE, IN THE LEE- WICK EXTENSION OF THE - - PowerPoint PPT Presentation

SLIDE 1

THE OTHER HIGGSES, AT RESONANCE, IN THE LEE- WICK EXTENSION OF THE STANDARD MODEL

ARXIV:1108.3765, JHEP10 (2011) 145 (IN COLLABORATION WITH ROMAN ZWICKY)

• Dr. Terrance Figy

The University of Manchester

Birmingham Particle Physics Seminars

29 Feb 2012

SLIDE 2

OUTLINE

• The Lee-Wick Standard Model
• Higgs boson pair production
• Top quark pair production
• Conclusions

SLIDE 3

LEE-WICK STANDARD MODEL (LWSM)

B.Grinstein, D.O’Connel, M.B.Wise (2007) Based on ideas by Lee and Wick (1969,1970)

SLIDE 4

A TOY MODEL

(A) HD formalism:

Lhd = 1 2∂µ ˆ φ∂µ ˆ φ − 1 2M2(∂2 ˆ φ)2 − 1 2m2 ˆ φ2 − 1 3!g ˆ φ3,

Propagator:

ˆ D(p) = i(p2 − p4/M 2 − m2)−1

2 poles: p2 = m2, M 2 (B) AF formalism: ˆ

φ = φ − ˜ φ

L = 1 2∂µφ∂µφ − 1 2∂µ ˜ φ∂µ ˜ φ + 1 2M2 ˜ φ2 − 1 2m2(φ − ˜ φ)2 − 1 3!g(φ − ˜ φ)3.

Wrong sign kinetic and mass term M. The two formulations are equivalent. Use EoM.

• B. Grinstein, D. O’Connel, M.B. Wise (2007)

SLIDE 5

A TOY MODEL

• B. Grinstein, D. O’Connel, M.B. Wise (2007)

φ φ φ + ˜ φ φ φ D(p) = i p2 − m2 ; ˜ D(p) = −i p2 − M2 Σ(0) = ig

• d4p

(2π)4 i p2 − m2−ig

• d4p

(2π)4 i p2 − M2 = ig

• d4p

(2π)4 i(m2 − M2) (p2 − m2)(p2 − M2) Quadratic divergence is cancelled leading to a logarithmic divergence.

SLIDE 6

A TOY MODEL

• B. Grinstein, D. O’Connel, M.B. Wise (2007)

D ˜

φ(p) =

−i p2 − M 2 + −i p2 − M 2

• −iΣ(p2)
• −i

p2 − M 2 + . . . = −i p2 − M 2 + Σ(p2).

D ˜

φ(p) =

−i p2 − M 2 − iMΓ, Γ = g2 32πM

• 1 − 4m2

M 2 .

A LW resonance has a probability of decaying in the interval .

Γdt −dt

Is this a problem? Shall we debate this issue further or proceed?

SLIDE 7

LWSM: SUMMARY

• For each SM field add a higher derivative (HD) term.
• Auxiliary fields (AF) can be introduced to cast the theory in terms of

interactions with mass dimension no greater than 4.

• The AFs are interpreted as LW partner states and have the wrong-sign

propagator (aka Pauli-Villars regulators).

• The LWSM solves the hierarchy problem: the extra minus sign in the loop

diagrams come from the LW field propagators. No need for opposite spin statistics!

• Unitarity is preserved, provided that the LW fields do no appear as

asymptotic states in the S-matrix.

• Causality is preserved at the the macroscopic level (where we live).

However, there can be violations of causality at the microscopic level.

SLIDE 8

1

• The Lee-Wick standard model - Grinstein, Benjamin et al. Phys.Rev. D77 (2008) 025012 . arXiv:0704.1845 [hep-ph] . CALT-68-2643, UCSD-PTH-07-04

2

• Negative Metric and the Unitarity of the S Matrix - Lee, T.D. et al. Nucl.Phys. B9 (1969) 209-243

3

• Finite Theory of Quantum Electrodynamics - Lee, T.D. et al. Phys.Rev. D2 (1970) 1033-1048

4

• Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model - Grinstein, Benjamin et al. Phys.Rev. D79 (2009) 105019 . arXiv:0805.2156 [hep-

th] . CALT-68-2684, UCSD-PTH-08-03

5

• A non-analytic S matrix - Cutkosky, R.E. et al. Nucl.Phys. B12 (1969) 281-300

6

• Vertex Displacements for Acausal Particles: Testing the Lee-Wick Standard Model at the LHC - Alvarez, Ezequiel et al. JHEP 0910 (2009) 023 . arXiv:0908.2446

[hep-ph] . UDEM-GPP-TH-09-183, IFIBA-TH-09-001

7

• Lee-wick Indefinite Metric Quantization: A Functional Integral Approach - Boulware, David G. et al. Nucl.Phys. B233 (1984) 1 . DOE/ER/40048-12 P3

8

• Non-perturbative quantization of phantom and ghost theories: Relating definite and indefinite representations - van Tonder, Andre Int.J.Mod.Phys. A22 (2007)

2563-2608 . hep-th/0610185

9

• Unitarity, Lorentz invariance and causality in Lee-Wick theories: An Asymptotically safe completion of QED - van Tonder, Andre . arXiv:0810.1928 [hep-th]

10 - Lee-Wick Theories at High Temperature - Fornal, Bartosz et al. Phys.Lett. B674 (2009) 330-335 . arXiv:0902.1585 [hep-th] . CALT-68-2720, UCSD-PTH-09-02 11 - Massive vector scattering in Lee-Wick gauge theory - Grinstein, Benjamin et al. Phys.Rev. D77 (2008) 065010 . arXiv:0710.5528 [hep-ph] . CALT-68-2662, UCSD-

PTH-07-10

12 - Neutrino masses in the Lee-Wick standard model - Espinosa, Jose Ramon et al. Phys.Rev. D77 (2008) 085002 . arXiv:0705.1188 [hep-ph] . CALT-68-2647, IFT-

UAM-CSIC-07-21, UCSD-PTH-07-05

13 - One-Loop Renormalization of Lee-Wick Gauge Theory - Grinstein, Benjamin et al. Phys.Rev. D78 (2008) 105005 . arXiv:0801.4034 [hep-ph] . UCSD-PTH-07-11 14 - Ultraviolet Properties of the Higgs Sector in the Lee-Wick Standard Model - Espinosa, Jose R. et al. Phys.Rev. D83 (2011) 075019 . arXiv:1101.5538 [hep-ph] 15 - A Higher-Derivative Lee-Wick Standard Model - Carone, Christopher D. et al. JHEP 0901 (2009) 043 . arXiv:0811.4150 [hep-ph] 16 - Higher-Derivative Lee-Wick Unification - Carone, Christopher D. Phys.Lett. B677 (2009) 306-310 . arXiv:0904.2359 [hep-ph] 17 - No Lee-Wick Fields out of Gravity - Rodigast, Andreas et al. Phys.Rev. D79 (2009) 125017 . arXiv:0903.3851 [hep-ph] . HU-EP-09-13 18 - A Nonsingular Cosmology with a Scale-Invariant Spectrum of Cosmological Perturbations from Lee-Wick Theory - Cai, Yi-Fu et al. Phys.Rev. D80 (2009)

023511 . arXiv:0810.4677 [hep-th]

19 - Searching for Lee-Wick gauge bosons at the LHC - Rizzo, Thomas G. JHEP 0706 (2007) 070 . arXiv:0704.3458 [hep-ph] . SLAC-PUB-12481 20 - Unique Identification of Lee-Wick Gauge Bosons at Linear Colliders - Rizzo, Thomas G. JHEP 0801 (2008) 042 . arXiv:0712.1791 [hep-ph] . SLAC-PUB-13039 21 - Flavor Changing Neutral Currents in the Lee-Wick Standard Model - Dulaney, Timothy R. et al. Phys.Lett. B658 (2008) 230-235 . arXiv:0708.0567 [hep-ph] .

CALT-68-2656

22 - Electroweak Precision Data and the Lee-Wick Standard Model - Underwood, Thomas E.J. et al. Phys.Rev. D79 (2009) 035016 . arXiv:0805.3296 [hep-ph] .

IPPP-08-21, DCPT-08-42

23 - Custodial Isospin Violation in the Lee-Wick Standard Model - Chivukula, R.Sekhar et al. Phys.Rev. D81 (2010) 095015 . arXiv:1002.0343 [hep-ph] .

MSUHEP-100201

24 - The Process gg ---> h(0) ---> gamma gamma in the Lee-Wick standard model - Krauss, F. et al. Phys.Rev. D77 (2008) 015012 . arXiv:0709.4054 [hep-ph] .

IPPP-07-49, DCPT-07-98

25 - Constraints on the Lee-Wick Higgs Sector - Carone, Christopher D. et al. Phys.Rev. D80 (2009) 055020 . arXiv:0908.0342 [hep-ph] 26 - Higgs ---> Gamma Gamma beyond the Standard Model - Cacciapaglia, Giacomo et al. JHEP 0906 (2009) 054 . arXiv:0901.0927 [hep-ph] . LYCEN-2008-13 27 - Collider Bounds on Lee-Wick Higgs Bosons - Alvarez, Ezequiel et al. Phys.Rev. D83 (2011) 115024 . arXiv:1104.3496 [hep-ph] . ZU-TH-06-11

References

SLIDE 9

Higgs Sector (AF formalism)

L = ( ˆ DµH)†( ˆ DµH) ( ˆ Dµ ˜ H)†( ˆ Dµ ˜ H) + M2

H ˜

H† ˜ H V (H ˜ H) ,

L where ˆ Dµ = ∂µ + i(Aµ + ˜ Aµ) w

h Aµ = gAa

µT a + g2W a µT a + g1Bµ Y

˜

gauge the two doublets are H> = ⇥ 0, (v + h0)/ p 2 ⇤ , ˜ H> = ⇥˜ h+, (˜ h0 + i˜ p0)/ p 2 ⇤

hh0i = v , h˜ h0i = 0 .

Lmass = λ 4 v2(h0 ˜ h0)2 + M2

H

2 (˜ h0˜ h0 + ˜ p0˜ p0 + 2˜ h+˜ h) . mixing between the Higgs scalar and its LW–partner. Th

LWSM

SLIDE 10

Higgs Sector

h ˜ h ! = cosh φh sinh φh sinh φh cosh φh ! hphys ˜ hphys !

h0 ˜ h0 ˜ p0 h± CP even even

• dd

none

m2

phys

M2

H

1 2

⇣ 1 q 1 2v2λ/M2

H

⌘

1 2

⇣ 1 + q 1 2v2λ/M2

H

⌘ 1 1

LWSM

Symplectic rotation: Mass eigenvalues:

SLIDE 11

Higgs Sector

LWSM

λv2 = 2m2

h0,phys

(1 + r2

h0) ,

rh0 ≡ mh0,phys m˜

h0,phys

,

sH = cosh φh = 1 (1 − r4

h0)1/2 ,

sH˜

H = cosh φh − sinh φh =

1 + r2

h0

(1 − r4

h0)1/2 .

Mixing angle:

SLIDE 12

Yukawa Interactions (in auxiliary field formalism)

L = Ψtiη3ˆ / DΨt − Ψt

RMtη3Ψt L − Ψt Lη3M†Ψt R ,

Ψt>

L = (TL, ˜

t0

L, ˜

TL) , Ψt>

R = (tR, ˜

tR, ˜ T 0

R)

SU(2) doublet: g. QL = (TL, BL)>

s which in turn form

Mtη3 = B @ mt −mt −mt −Mu mt −MQ 1 C A , η3 = B @ 1 0 0 −1 0 0 0 −1 1 C A

LWSM

SLIDE 13

Diagonalization of mass matrices

ΨL(R),phys = η3S†

L(R)η3ΨL(R) ,

Mt,physη3 = S†

RMtη3SL ,

SLη3S†

L = η3

and SRη3S†

R = η3

L = −1 v(h0 − ˜ h0) ⇣ Ψt

RgtΨt L + Ψt Lg† tΨt R

⌘ − 1 v(−i˜ p0) ⇣ Ψt

RgtΨt L − Ψt Lg† tΨt R

⌘

gt = B @ mt 0 −mt −mt 0 mt 1 C A , gt,phys = S†

RgtSL

Higgs-quark vertices

LWSM

SLIDE 14

LWSM

L2g = − 1 2Tr

• BµνBµν − ˜

Bµν ˜ Bµν + WµνW µν − ˜ W µν ˜ W µν − 1 2(M1

2 ˜

Bµ ˜ Bµ + M2

2 ˜

W a

µ ˜

W µ

a) + g2 2v2

8 (W 1,2

µ

+ ˜ W 1,2

µ )2

+ v2 8 (g1Bµ + g1 ˜ Bµ + g2W 3

µ + g2 ˜

W 3

µ)2

LW gauge bosons are massive and mix: Lint = −

• ψ=qL,uR,dR

[g1 ¯ ψ(B + ˜ B)ψ + g2 ¯ ψ(W + ˜ W )ψ] +

• ψ=q,u,d
• g1¯

˜ ψ(B + ˜ B)˜ ψ + g2¯ ˜ ψ(W + ˜ W ) ˜ ψ

• .

Gauge interactions:

SLIDE 15

LWSM

g2

˜ Pgg =

σ(gg → ˜ P) σSM(gg → H) = | g ˜

Pt¯ t F ˜ P 1/2(βt ˜ P)

F1/2(βt

˜ P)

|2 ,

gh0f ¯

f = −g˜ h0f ¯ f = cosh θ − sinh θ =

1 + r2 √ 1 − r4 , g ˜

Pf ¯ f = −1 .

Couplings to gauges bosons and fermions

• E. Alvarez, E. Coluccio, J.Zurita: arXiv 1004.3496

SLIDE 16

LW Gauge bosons at the LHC

m [TeV]

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 B [pb] σ

• 3

10

• 2

10

• 1

10 1

Expected limit σ 1 ± Expected σ 2 ± Expected Observed limit

SSM

Z’

χ

Z’

ψ

Z’

ATLAS ll → Z’ = 7 TeV s

• 1

L dt = 1.08 fb

∫

ee:

• 1

L dt = 1.21 fb

∫

: µ µ

ArXiv:1108.1582

[GeV]

W’

m 500 1000 1500 B [pb] σ

• 2

10

• 1

10 1 10

NNLO theory Observed limit Expected limit σ 1 ± Expected σ 2 ± Expected

= 7 TeV, s

∫

• 1

= 7 TeV, Ldt = 36 pb s ν l → W’ ATLAS

ArXiv:1103.1391

SLIDE 17

Electroweak Precision Constraints

(a)

1000 2000 3000 4000 5000 6000 1000 2000 3000 4000 5000 6000 M1 GeV M2 GeV mH 115 GeV LEP1 SLC 90,99 C.L. 2 dof

(b)

1000 2000 3000 4000 5000 6000 1000 2000 3000 4000 5000 6000 M1 GeV M2 GeV mH 115 GeV LEP2 90,99 C.L. 2 dof

T.E.J. Underwood and R. Zwicky (2009)

SLIDE 18

LWSM HIGGS CONSTRAINTS

B → Xsγ

C.D. Carone and R. Primulando (2009)

m2

h0 + m2 ˜ h0 = m2 ˜ p0 = m2 ˜ h± > (463 GeV)2

SLIDE 19

Electroweak Precision Constraints

¼ 95 CL 2 d.o.f.

2 4 6 8 10 2 4 6 8 10 Mq TeV Mt TeV 1.45 TeV 2.4 TeV mh 115 GeV mh 800 GeV 4 2 2 4 4 2 2 4 1000 S 1000 T

• FIG. 6 (color online).

Left: 95% C.L. exclusion plots for the LW fermion masses Mq and Mt. These bounds come almost entirely from the experimental constraints on ^

• T. For a light Higgs the striped region to the left of the curve is excluded, while a heavy Higgs is

completely excluded. Right: 95% C.L. ellipses in the ð ^ S; ^ TÞ plane, and the LW prediction for degenerate masses, Mq ¼ Mt. The parametric plot is for 0:5 TeV < Mq < 10 TeV and the dots are equally spaced in mass. The lower bound on Mq is approximately 1.5 TeV for a light Higgs.

R.S. Chivukula, A. Farzinnia, R. Foadi, and E.H.Simmons (2010)

A heavy light Higgs boson is disfavored.

SLIDE 20

LWSM HIGGS CONSTRAINTS

Excluded by LEP Excluded by Tevatron

“LEP reach” Currently allowed

None analysis apply

Perturbativity bound HiggsBounds 2.1.1: P . Bechtle, O. Brein, S. Heinemeyer,

• G. Weiglein, K. E. Williams (2008-2011)

b → XSγ

• E. Alvarez, E. Coluccio, J.Zurita: arXiv 1004.3496

SLIDE 21

LIGHT HIGGS BOSON AT THE LHC

L = 1, 5, 10 fb−1: end of 2011, end of 2012, optimistic

h0 → WW : mh0 ≥ 130/125/120 GeV

Other Higgs bosons and channels are out of LHC Run I reach.

• E. Alvarez, E. Coluccio, J.Zurita: arXiv 1004.3496

SLIDE 22

LIGHT HIGGS BOSON AT THE LHC

pp Æ H Æ WW pp Æ H Æ gg pp Æ H Æ ZZ VH, H Æ bb qqH, H Æ t+t- pp Æ H Æ t+t-

100 500 200 300 150 0.10 1.00 0.50 5.00 0.20 2.00 0.30 3.00 0.15 1.50 0.70

MH @GeVD 95 % C.L. limit on sêsSM LHC û 7 TeV, 15 fb-1 HATLAS+CMSL

pp Æ H Æ WW pp Æ H Æ gg pp Æ H Æ ZZ VH, H Æ bb qqH, H Æ t+t- pp Æ H Æ t+t-

100 500 200 300 150 1.0 10.0 5.0 50.0 2.0 20.0 3.0 30.0 1.5 15.0 7.0

MH @GeVD Statistical Significance LHC û 7 TeV, 15 fb-1 HATLAS+CMSL

• E. Weihs and J. Zurita (2011)

The minimal LWSM can be ruled out by searching for the light Higgs boson at the LHC.

SLIDE 23

LIGHT HIGGS BOSON AT THE LHC

(a)

[GeV]

H

M 110 115 120 125 130 135 140 145 150 Local P-Value

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10 1 Observed Expected σ 2 σ 3 σ 4 σ 5 = 7 TeV s

• 1

Ldt = 1.0-4.9 fb

∫

ATLAS Preliminary 2011 Data

(b)

[GeV]

H

M 110 115 120 125 130 135 140 145 150 Signal strength

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 2.5 Best fit σ 1 ± = 7 TeV s

• 1

Ldt = 1.0-4.9 fb

∫

ATLAS Preliminary 2011 Data

(b)

ATL-CONF-2011-163 CMS PAS HIG-11-032

)

2

Higgs boson mass (GeV/c

110 115 120 125 130 135 140 145 150 155 160

Local p-value

• 4

10

• 3

10

• 2

10

• 1

10 1

σ 1 σ 2 σ 3 σ 4

Combined )

• 1

bb (4.7 fb → H )

• 1

(4.6 fb τ τ → H )

• 1

(4.7 fb γ γ → H )

• 1

WW (4.6 fb → H )

• 1

4l (4.7 fb → ZZ → H )

• 1

2l 2q (4.6 fb → ZZ → H

elsewhere effect correction Interpretation requires look- = 7 TeV s CMS Preliminary,

) Higgs boson mass (GeV/c )

2

Higgs boson mass (GeV/c

110 115 120 125 130 135 140 145 150 155 160

SM

σ / σ Best fit

• 1
• 0.5

0.5 1 1.5 2 2.5

from fit σ 1 ± from fit σ 1 ±

• 1

= 4.6-4.7 fb

int

Combined, L = 7 TeV s CMS Preliminary,

SLIDE 24

C.D. Carone and R. F. Lebed (2008)

A Higher Derivative LWSM

LHD = ˆ Dµ ˆ H† ˆ Dµ ˆ H − m2

H ˆ

H† ˆ H − 1 M2

1

ˆ H†( ˆ Dµ ˆ Dµ)2 ˆ H − 1 M4

2

ˆ H†( ˆ Dµ ˆ Dµ)3 ˆ H + Lint( ˆ H)

L = −H(1)†( ˆ Dµ ˆ Dµ + m2

1)H(1) + H(2)†( ˆ

Dµ ˆ Dµ + m2

2)H(2)

−H(3)†( ˆ Dµ ˆ Dµ + m2

3)H(3) + Lint( ˆ

H) ,

H(1) =  

1 √ 2(v + h1)

  , H(2) =   h+

2 1 √ 2(h2 + iP2)

  , H(3) =   h+

3 1 √ 2(h3 + iP3)

  ,

3 Higgs doublet model with

• ne negative norm state and

two positive norm states. We leave this for further study and focus on the minimal LWSM.

SLIDE 25

HIGGS BOSON PAIR PRODUCTION

(a)

g g h0 h0 h0, ˜ h0 qi qi qi

(b)

g g h0 h0 qi qi qi qj

pp → h0h0

→ M(gg → h0h0) = 1 32π2 δab g2 v2 ⇣ A0P0 + A2P2 ⌘

µνe(p1)µ a e(p2)ν b

For details see our Appendix!

SLIDE 26

HIGGS BOSON PAIR PRODUCTION

0.1 1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

S 1/2 = 7 TeV 0.1 1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

S 1/2 = 7 TeV mh0 = 120 GeV mh0 = 150 GeV mh0 = 200 GeV mh0 = 120 GeV mh0 = 150 GeV mh0 = 200 GeV SM: mh0 = 120 GeV SM: mh0 = 150 GeV SM: mh0 = 200 GeV 1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

S 1/2 = 14 TeV 1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

S 1/2 = 14 TeV mh0 = 120 GeV mh0 = 150 GeV mh0 = 200 GeV mh0 = 120 GeV mh0 = 150 GeV mh0 = 200 GeV SM: mh0 = 120 GeV SM: mh0 = 150 GeV SM: mh0 = 200 GeV

Total cross section

SLIDE 27

HIGGS BOSON PAIR PRODUCTION

Total cross section

1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

mh0 = 120 GeV S 1/2 = 7 TeV 1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

mh0 = 120 GeV S 1/2 = 7 TeV MQ = 500 GeV MQ = 700 GeV MQ = 1000 GeV MQ = 500 GeV MQ = 700 GeV MQ = 1000 GeV SM 1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

mh0 = 120 GeV S 1/2 = 14 TeV 1 10 100 1000 10000 200 300 400 500 600 700 800 900 1000 σ (fb) m˜

h0 (GeV)

mh0 = 120 GeV S 1/2 = 14 TeV MQ = 500 GeV MQ = 700 GeV MQ = 1000 GeV MQ = 500 GeV MQ = 700 GeV MQ = 1000 GeV SM

SLIDE 28

HIGGS BOSON PAIR PRODUCTION

1 0.5 1 1 2 2 3

200 300 400 500 600 700 800 100 200 300 400 500 600 mh

• mh0

7 TeV

1 3 LogΣfb 0.5 1 2 2 3 3 4

200 300 400 500 600 700 800 100 200 300 400 500 600 mh

• mh0

14 TeV

0.5 4 LogΣfb

Total cross section

SLIDE 29

HIGGS BOSON PAIR PRODUCTION

• 5
• 4
• 3
• 1

200 300 400 500 600 700 800 100 120 140 160 180 200 220 240 mh

é

mh0 7 TeV

• 5

1 Log@sHfbLD

• 4
• 4
• 3
• 2

1

200 300 400 500 600 700 800 100 120 140 160 180 200 220 240 mh

é

mh0 14 TeV

• 4

1 Log@sHfbLD

pp → h0h0 → b¯ bγγ

SLIDE 30

HIGGS BOSON PAIR PRODUCTION

pp → h0h0 → b¯ bγγ

• Cut 1: Two isolated photons.
• Cut 2: Two kt jets.
• Cut 3: At least one b-tagged jet.
• Cut 4:
• Cut 5:
• Cut 6:

|Mγγ − mh0| ≤ 2 GeV |Mbj − mh0| ≤ 20 GeV |Mbjγγ − m˜

h0| ≤ δm˜ h0

Cuts inspired by radion studies performed by ATLAS and CMS. A more detailed description of cuts is in our paper.

SLIDE 31

HIGGS BOSON PAIR PRODUCTION

pp → h0h0 → b¯ bγγ

h0h0 → γγb¯ b γγbb (QCD+EW) 100 200 300 400 500 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 pγ1

T [GeV]

Arbitrary h0h0 → γγb¯ b γγbb (QCD+EW) 100 200 300 400 500 0.05 0.1 0.15 0.2 0.25 0.3 0.35 pj1

T [GeV]

Arbitrary

h0h0 → γγb¯ b Backgrounds 300 400 500 600 700 800 1 2 3 4 5 6 7 8 9 mh0 = 120 GeV, m˜

h0 = 300 GeV

Mbjγγ[GeV] dN/dMbjγγ[Events/8 GeV/30 fb−1]

SLIDE 32

HIGGS BOSON PAIR PRODUCTION

pp → h0h0 → b¯ bγγ

Benchmark mh0(GeV) m˜

h0(GeV)

m˜

h0(GeV)

(a) 120 300 40 (b) 130 445 45 (c) 130 550 50 QCD+EW: jj bb cc bc bj cj gen(pb) 23.2 0.176 1.56 0.0840 0.519 6.26 cut 1 0.390 0.370 0.306 0.295 0.344 0.354 cut 2 0.363 0.358 0.386 0.435 0.406 0.366 cut 3 0.0526 0.795 0.116 0.516 0.460 0.0920 cut 4a 0.0212 0.0233 0.0247 0.0217 0.0240 0.0200 cut 5a 0.249 0.229 0.232 0.242 0.264 0.203 cut 6a 0.604 0.547 0.713 0.534 0.471 0.627 ✏tot 2.37 × 10−5 3.07 × 10−4 5.60 × 10−5 1.85 × 10−4 1.93 × 10−4 3.03 × 10−5 (a) eff(fb) 0.550 0.0527 0.0873 0.0156 0.100 0.190 cut 4b 0.0150 0.0202 0.0139 0.0167 0.0221 0.0191 cut 5b 0.221 0.213 0.174 0.242 0.234 0.276 cut 6b 0.136 0.0567 0.129 0.138 0.165 0.130 ✏tot 3.37 × 10−6 2.56 × 10−5 6.14 × 10−6 3.67 × 10−5 5.46 × 10−5 8.06 × 10−6 (b) eff(fb) 0.0782 0.00431 0.00959 0.00309 0.0283 0.0505 cut 4c 0.0150 0.0213 0.0199 0.0167 0.0221 0.0191 cut 5c 0.221 0.213 0.174 0.242 0.234 0.274 cut 6c 0.00723 0.0337 0.00289 0.0164 0.0303. 0.0.0122 ✏tot 1.79 × 10−7 1.52 × 10−5 1.38 × 10−8 4.36 × 10−6 1.00 × 10−5 7.58 × 10−7 (c) eff(fb) 0.00414 0.00261 2.15 × 10−5 0.000366 0.00521 0.00475

SLIDE 33

HIGGS BOSON PAIR PRODUCTION

pp → h0h0 → b¯ bγγ

Benchmark mh0(GeV) m˜

h0(GeV)

m˜

h0(GeV)

(a) 120 300 40 (b) 130 445 45 (c) 130 550 50

pp → h0h0 → b¯ b (a) (b) (c) gen(fb) 11.2 0.964 0.195 cut 1 0.594 0.675 0.693 cut 2 0.414 0.405 0.391 cut 3 0.734 0.760 0.748 cut 4 0.999 0.999 0.999 cut 5 0.601 0.567 0.586 cut 6 0.966 0.823 0.725 ✏tot 0.105 0.097 0.0861 eff(fb) 1.18 0.0935 0.0168

tot

pp → h0Z → b¯ b (a) mh0 = 120 GeV, m˜

h0 = 300 GeV

gen(fb) 32.3 cut 1 0.745 cut 2 0.489 cut 3 0.772 cut 4 0.999 cut 5 0.184 cut 6 0.422 ✏tot 0.0218 eff(fb) 0.703

SLIDE 34

HIGGS BOSON PAIR PRODUCTION

pp → h0h0 → b¯ bγγ

Benchmark mh0(GeV) m˜

h0(GeV)

m˜

h0(GeV)

(a) 120 300 40 (b) 130 445 45 (c) 130 550 50

10 20 30 40 50 LintH1êfbL 1 2 3 4 5 S B + S 500 1000 1500 2000 2500 3000 LintH1êfbL 2 4 6 8 10 S B + S

√

SLIDE 35

INTERFERENCE EFFECTS IN TOP PAIR PRODUCTION

dˆ σ ds (gg → ¯ tt)|interference = −|c(s)|Re  l4 s − m2

R + imRΓR

• = −|˜

c(s)|

• (s − m2

R)Re[l4] + mRΓRIm[l4]

• D.Dicus, A. Strange, and S. Willenbrock

gg → R → ¯ tt

loop triangle function

l4 = l4(s/4m2

t)

• 1. If there is no loop function there will be a peak-dip.
• 2. For a scalar or pseudo-scalar resonance this pattern does

not change.

SLIDE 36

INTERFERENCE EFFECTS IN TOP PAIR PRODUCTION

gg → R → ¯ tt

agator and the width, dˆ σ ds (gg → ¯ tt)|LWinterference = −|c(s)|Re  −l4(s/4m2

t )

(s − m2

R) − imRΓR

• = −|˜

c(s)|

• −(s − m2

R)Re[l4] + mRΓRIm[l4]

• Sign-flip in the LW

case

M2

R = m2 R + Im[l4]

Re[l4]mRΓR

Dip-peak structure

SLIDE 37

400 500 600 700 800 sHGeVL 8 9 10 11 12 13 s Hgg Æ ttL 400 500 600 700 800 sHGeVL 8 9 10 11 12 13 s Hgg Æ ttL

Usual resonance Lee-Wick type resonance Peak-dip Dip-peak

INTERFERENCE EFFECTS IN TOP PAIR PRODUCTION

SLIDE 38

QCD gg → ˜ h0 → ¯ tt gg → ˜ p0 → ¯ tt gg → ˜ h0, ˜ p0 → ¯ tt 300 400 500 600 700 800 900 1000 0.5 1 1.5 2 2.5 3 LO, MSTW2008 LO(90% C.L.), √ S = 14 TeV, µ f = µr = mt Mtt[GeV] dσ/dMtt[pb/GeV] QCD gg → ˜ h0 → ¯ tt gg → ˜ p0 → ¯ tt gg → ˜ h0, ˜ p0 → ¯ tt 300 400 500 600 700 800 900 1000 0.5 1 1.5 2 2.5 3 LO, MSTW2008 LO(90% C.L.), √ S = 14 TeV, µ f = µr = mt Mtt[GeV] dσ/dMtt[pb/GeV] QCD gg → ˜ h0 → ¯ tt gg → ˜ p0 → ¯ tt gg → ˜ h0, ˜ p0 → ¯ tt 300 400 500 600 700 800 900 1000 0.5 1 1.5 2 2.5 3 LO, MSTW2008 LO(90% C.L.), √ S = 14 TeV, µ f = µr = mt Mtt[GeV] dσ/dMtt[pb/GeV] QCD gg → ˜ h0, ˜ p0 → ¯ tt 500 600 700 800 900 1000 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 LO, MSTW2008 LO(90% C.L.), √ S = 14 TeV, µ f = µr = mt Mtt[GeV] dσ/dMtt[pb/GeV]

Top pair invariant mass spectrum

pT > 250 GeV

SLIDE 39

CONCLUSIONS

• LW Gauge bosons and LW fermions are constrained to be in the few TeV range by EWPO and di-

lepton searches while the LW Higgs could be below a TeV.

• We have computed the total cross section for double Higgs boson pair production.
• Additionally, we have investigated a search at the a 14 TeV LHC using the di-photon plus di-jet
• channel. For LW Higgs boson masses of 300 GeV a 5 sigma discovery can be made with 20 1/fb
• f integrated luminosity.
• We have investigated top pair production in the LWSM. For LW Higgs boson masses above the

top pair production threshold, the branching fraction of the LW Higgs boson decaying top pairs

• dominates. Hence, the top pair channel dominates over the double Higgs boson channel.

SLIDE 40

Higgs boson decays

0.0001 0.001 0.01 0.1 1 100 120 140 160 180 200 Brh0 mh0 (GeV) γγ gg b¯ b c¯ c τ+τ− W+W− ZZ 0.001 0.01 0.1 1 200 300 400 500 600 700 800 900 1000 Br˜

h0

m˜

h0 (GeV)

h0h0 t¯ t b¯ b W+W− ZZ

Figure 15. (left,right) Branching ratios Br and Br as a function of the masses m and m and

0.01 0.1 1 10 100 200 300 400 500 600 700 800 900 1000 Γ˜

h0 (GeV)

m˜

h0 (GeV)

mh0 = 120 GeV MQ = 500 GeV MQ = 700 GeV MQ = 1000 GeV

SLIDE 41

F.Krauss, T.E.J Underwood, R. Zwicky: arXiv 0709.4054

120 140 160 180 200 0.0 0.1 0.2 0.3 0.4 mh0,phys GeV Κgg

2 ΚΓΓ 2 1

M

• 500 GeV

M

• 750 GeV

M

• 1000 GeV

Figure 4: The relative change in the cross-section times decay rate for the full process gg →

h0 → γγ in the LWSM, expressed as |κgg|2|κγγ|2 −1, plotted as a function of mh0,phys. Lee-Wick mass scales are such that MQ = Mu = m˜

h,phys = m˜ h+,phys = m ˜ W,phys ≡ ˜

M

Higgs to two photons